Midpoints And Segment Bisectors Worksheet Answers - Free Printable

It looks like you've uploaded an image titled "Midpoints and Segment Bisectors" with a line segment labeled AB, and a coordinate grid below it. However, the image doesn't include any specific coordinates for points A and B, nor does it show any additional instructions or questions.

To help you solve the problem, I’ll explain what midpoints and segment bisectors are and how to find them — assuming this is a typical geometry task involving these concepts.

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🔹 What is a Midpoint?

The midpoint of a line segment is the point that divides the segment into two equal parts. It is exactly halfway between the two endpoints.

If the endpoints of a segment are:
- $ A(x_1, y_1) $
- $ B(x_2, y_2) $

Then the midpoint M is given by the formula:

$$
M = \left( \frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2} \right)
$$

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🔹 What is a Segment Bisector?

A segment bisector is any line, ray, or segment that passes through the midpoint of a segment and divides it into two congruent (equal) parts.

- A perpendicular bisector is a special type of bisector that intersects the segment at a 90-degree angle at the midpoint.

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🔹 How to Solve This Problem (Assuming Typical Task)

Since your image shows a segment AB and a coordinate grid, here’s what you might be expected to do:

#### Step 1: Identify Coordinates of A and B
Even though they’re not labeled in your image, if this were a full problem, you would likely have:
- Point A at some coordinate, e.g., $ A(-4, 2) $
- Point B at another, e.g., $ B(6, -2) $

Let’s assume some example values (since none are given):

Let’s say:
- $ A = (-4, 2) $
- $ B = (6, -2) $

#### Step 2: Find the Midpoint

Use the midpoint formula:

$$
M = \left( \frac{-4 + 6}{2}, \frac{2 + (-2)}{2} \right) = \left( \frac{2}{2}, \frac{0}{2} \right) = (1, 0)
$$

So, the midpoint is $ (1, 0) $.

#### Step 3: Draw or Find the Perpendicular Bisector

To draw the perpendicular bisector:
1. Plot the midpoint $ (1, 0) $.
2. Find the slope of AB:
$$
m_{AB} = \frac{-2 - 2}{6 - (-4)} = \frac{-4}{10} = -\frac{2}{5}
$$
3. The slope of the perpendicular bisector is the negative reciprocal:
$$
m_{\perp} = \frac{5}{2}
$$
4. Use point-slope form to write the equation of the perpendicular bisector:
$$
y - 0 = \frac{5}{2}(x - 1) \Rightarrow y = \frac{5}{2}x - \frac{5}{2}
$$

This line passes through the midpoint and is perpendicular to AB — so it's the perpendicular bisector.

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✔ Summary

Without specific coordinates, here’s what you should do:

1. Find the midpoint using the midpoint formula.
2. Draw or describe the perpendicular bisector:
- It goes through the midpoint.
- It is perpendicular to segment AB.

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📌 Final Note:

Please provide:
- The actual coordinates of points A and B, or
- Any question asked in the original task (e.g., "Find the midpoint", "Construct the bisector", etc.)

Then I can give you the exact solution!

Let me know if you’d like to add more details!